Soit une fonction radiale, non négative, localement intégrable sur , qui ne s’accroît pas en . Posons où et . Étant donné et , nous démontrons qu’il existe de sorte que pour tout , si et seulement si, existe avec pour tout cube dyadique , où .
On se sert de ce résultat pour raffiner des approximations récentes de la part de C.L. Fefferman et D.H. Phong de la distribution de valeurs propres d’opérateurs de Schrödinger.
Suppose is a nonnegative, locally integrable, radial function on , which is nonincreasing in . Set when and . Given and , we show there exists so that for all , if and only if exists with for all dyadic cubes Q, where . This result is used to refine recent estimates of C.L. Fefferman and D.H. Phong on the distribution of eigenvalues of Schrödinger operators.
@article{AIF_1986__36_4_207_0, author = {Kerman, R. and Sawyer, Eric T.}, title = {The trace inequality and eigenvalue estimates for {Schr\"odinger} operators}, journal = {Annales de l'Institut Fourier}, pages = {207--228}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {36}, number = {4}, year = {1986}, doi = {10.5802/aif.1074}, mrnumber = {88b:35150}, zbl = {0591.47037}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.1074/} }
TY - JOUR AU - Kerman, R. AU - Sawyer, Eric T. TI - The trace inequality and eigenvalue estimates for Schrödinger operators JO - Annales de l'Institut Fourier PY - 1986 SP - 207 EP - 228 VL - 36 IS - 4 PB - Institut Fourier PP - Grenoble UR - http://archive.numdam.org/articles/10.5802/aif.1074/ DO - 10.5802/aif.1074 LA - en ID - AIF_1986__36_4_207_0 ER -
%0 Journal Article %A Kerman, R. %A Sawyer, Eric T. %T The trace inequality and eigenvalue estimates for Schrödinger operators %J Annales de l'Institut Fourier %D 1986 %P 207-228 %V 36 %N 4 %I Institut Fourier %C Grenoble %U http://archive.numdam.org/articles/10.5802/aif.1074/ %R 10.5802/aif.1074 %G en %F AIF_1986__36_4_207_0
Kerman, R.; Sawyer, Eric T. The trace inequality and eigenvalue estimates for Schrödinger operators. Annales de l'Institut Fourier, Tome 36 (1986) no. 4, pp. 207-228. doi : 10.5802/aif.1074. http://archive.numdam.org/articles/10.5802/aif.1074/
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